We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B,... ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for non-commutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, � , •) acts on an underlying Q-right module (M, � ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A: M → M and f Q A: Q → Q of (lax) morphisms for each agent A ∈ A. By adjunction, they give rise to epistemic modalities [12], capturing the agents ’ knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [20] — cf. weakest preconditions. This model subsumes the crucial fragment of Baltag, Moss and Solecki’s [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resource-sensitive structure on the epistemic actions. Keywords: Multi-agent communication, knowledge update, resource-sensitivity, quantale, Galois adjoints, dynamic epistemic logic, sequent calculus, Lambek calculus, Linear Logic.

To describe simultaneous knowledge updates for different subgroups we propose an epistemic language with dynamic operators for actions. The language is interpreted on equivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and local choice. Learning is the dynamic equivalent of common knowledge. Local choice aids in constraining the interpretation of an action to a functional interpretation (state transformer). Bisimilarity is preserved under execution of actions. The language is applied to describe various actions in card games.

The paper deals with credible and relevant information flow in dialogs: How useful is it for a receiver to get some information, how useful is it for a sender to give this information, and how much credible information can we expect to flow between sender and receiver? What is the relation between semantics and pragmatics? These Gricean questions will be addressed from a decision and game-theoretical point of view.

Abstract. The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models [3], now in widespread use (see [10] for a textbook treatment). There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of structural equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect, provided we confine attention to ‘smooth ’ action models. We also give a recipe for turning any action model into a smooth one with the same update effect. Together, this yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action. 1.

In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is `fact p is true and you don't know that', after which you know that p,which entails the negation of the announcement formula. The announcement of such a formula in a given information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and `philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas.

We introduce an algebraic approach to Dynamic Epistemic Logic. This approach has the advantage that: (i) its semantics is a transparent algebraic object with a minimal set of primitives from which most ingredients of Dynamic Epistemic Logic arise, (ii) it goes with the introduction of non-determinism, (iii) it naturally extends beyond boolean sets of propositions, up to intuitionistic and non-distributive situations, hence allowing to accommodate constructive computational, information-theoretic as well as non-classical physical settings, and (iv) introduces a structure on the actions, which now constitute a quantale. We also introduce a corresponding sequent calculus (which extends Lambek calculus), in which propositions, actions as well as agents appear as resources in a resource-sensitive dynamic-epistemic logic.

Abstract. If we are to take the notion of speech act seriously, we must be able to treat speech acts as acts. In this paper, we will try to model changes brought about by various acts of commanding in terms of a variant of update logic. We will combine a multi-agent variant of the language of monadic deontic logic with a dynamic language to talk about the situations before and after the issuance of commands, and the commands that link those situations. Although the resulting logic inherits various inadequacies from monadic deontic logic, some interesting principles are captured and seen to be valid nonetheless. A complete axiomatization and some interesting valid principles together with concrete examples will be presented, and suggestions for further research will be made. 1

We develop a conceptual and formal clarification of the notion of surprise as a belief-based phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of the cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatch-based surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in psychology of emotion. We provide several comparisons of our approach with those models.

Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [5]), Epistemic-

Dynamic epistemic logic is the logic of the effects of epistemic actions like making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [4], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modeling tool DEMO [10]. DEMO allows modeling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, and translation of dynamic epistemic formulas to PDL [22] formulas. DEMO is written in Haskell. This paper intends to demonstrate its usefulness for visualizing the model transformations that take place during epistemic updating. Project paper, on the application of functional programming in a new area. 1